Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4100,2,Mod(1149,4100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4100, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4100.1149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4100 = 2^{2} \cdot 5^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4100.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.7386648287\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 2x^{6} + 4x^{5} + 14x^{4} - 14x^{3} + 8x^{2} + 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 164) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1149.2 | ||
Root | \(-0.187509 + 0.187509i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4100.1149 |
Dual form | 4100.2.d.c.1149.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4100\mathbb{Z}\right)^\times\).
\(n\) | \(1477\) | \(2051\) | \(3901\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − 2.92968i | − 1.69145i | −0.533618 | − | 0.845726i | \(-0.679168\pi\) | ||||
0.533618 | − | 0.845726i | \(-0.320832\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.77840i | 1.05014i | 0.851060 | + | 0.525069i | \(0.175960\pi\) | ||||
−0.851060 | + | 0.525069i | \(0.824040\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −5.58303 | −1.86101 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.02837 | 0.611575 | 0.305788 | − | 0.952100i | \(-0.401080\pi\) | ||||
0.305788 | + | 0.952100i | \(0.401080\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.10932i | 0.862371i | 0.902263 | + | 0.431186i | \(0.141905\pi\) | ||||
−0.902263 | + | 0.431186i | \(0.858095\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 7.91609i | − 1.91993i | −0.280112 | − | 0.959967i | \(-0.590372\pi\) | ||||
0.280112 | − | 0.959967i | \(-0.409628\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.17964 | −0.500044 | −0.250022 | − | 0.968240i | \(-0.580438\pi\) | ||||
−0.250022 | + | 0.968240i | \(0.580438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 8.13983 | 1.77626 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.75004i | 0.990451i | 0.868764 | + | 0.495226i | \(0.164915\pi\) | ||||
−0.868764 | + | 0.495226i | \(0.835085\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.56744i | 1.45636i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.85936 | −0.716665 | −0.358333 | − | 0.933594i | \(-0.616655\pi\) | ||||
−0.358333 | + | 0.933594i | \(0.616655\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.6661 | −1.91569 | −0.957847 | − | 0.287280i | \(-0.907249\pi\) | ||||
−0.957847 | + | 0.287280i | \(0.907249\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 5.94246i | − 1.03445i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.58303i | 1.08224i | 0.840944 | + | 0.541122i | \(0.182000\pi\) | ||||
−0.840944 | + | 0.541122i | \(0.818000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 9.10932 | 1.45866 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 4.80677i | − 0.733025i | −0.930413 | − | 0.366513i | \(-0.880552\pi\) | ||||
0.930413 | − | 0.366513i | \(-0.119448\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.03900i | 0.589149i | 0.955628 | + | 0.294575i | \(0.0951779\pi\) | ||||
−0.955628 | + | 0.294575i | \(0.904822\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.719526 | −0.102789 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −23.1916 | −3.24748 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.94327i | 0.266928i | 0.991054 | + | 0.133464i | \(0.0426101\pi\) | ||||
−0.991054 | + | 0.133464i | \(0.957390\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.38566i | 0.845801i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.75004 | −0.618402 | −0.309201 | − | 0.950997i | \(-0.600062\pi\) | ||||
−0.309201 | + | 0.950997i | \(0.600062\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.89068 | 0.370113 | 0.185057 | − | 0.982728i | \(-0.440753\pi\) | ||||
0.185057 | + | 0.982728i | \(0.440753\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 15.5119i | − 1.95432i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.97163i | 0.729551i | 0.931095 | + | 0.364776i | \(0.118854\pi\) | ||||
−0.931095 | + | 0.364776i | \(0.881146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 13.9161 | 1.67530 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.4026 | 1.70927 | 0.854636 | − | 0.519228i | \(-0.173780\pi\) | ||||
0.854636 | + | 0.519228i | \(0.173780\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.24916i | 1.08253i | 0.840851 | + | 0.541266i | \(0.182055\pi\) | ||||
−0.840851 | + | 0.541266i | \(0.817945\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.63562i | 0.642238i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.320282 | 0.0360345 | 0.0180173 | − | 0.999838i | \(-0.494265\pi\) | ||||
0.0180173 | + | 0.999838i | \(0.494265\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.42111 | 0.602346 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.69745i | 0.405847i | 0.979195 | + | 0.202924i | \(0.0650443\pi\) | ||||
−0.979195 | + | 0.202924i | \(0.934956\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.3067i | 1.21220i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.96868 | −0.950679 | −0.475339 | − | 0.879803i | \(-0.657675\pi\) | ||||
−0.475339 | + | 0.879803i | \(0.657675\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.63895 | −0.905608 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 31.2484i | 3.24030i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.8322i | 1.81058i | 0.424790 | + | 0.905292i | \(0.360348\pi\) | ||||
−0.424790 | + | 0.905292i | \(0.639652\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −11.3244 | −1.13815 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −13.0254 | −1.29608 | −0.648039 | − | 0.761607i | \(-0.724410\pi\) | ||||
−0.648039 | + | 0.761607i | \(0.724410\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 8.05673i | 0.793853i | 0.917850 | + | 0.396927i | \(0.129923\pi\) | ||||
−0.917850 | + | 0.396927i | \(0.870077\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 4.41602i | − 0.426912i | −0.976953 | − | 0.213456i | \(-0.931528\pi\) | ||||
0.976953 | − | 0.213456i | \(-0.0684721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.5255 | −1.77442 | −0.887210 | − | 0.461366i | \(-0.847360\pi\) | ||||
−0.887210 | + | 0.461366i | \(0.847360\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 19.2862 | 1.83056 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 8.08310i | 0.760394i | 0.924905 | + | 0.380197i | \(0.124144\pi\) | ||||
−0.924905 | + | 0.380197i | \(0.875856\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 17.3594i | − 1.60488i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 21.9941 | 2.01620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.88573 | −0.625976 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.92968i | 0.264160i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.44748i | 0.394650i | 0.980338 | + | 0.197325i | \(0.0632255\pi\) | ||||
−0.980338 | + | 0.197325i | \(0.936775\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.0823 | −1.23988 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.85936 | 0.861416 | 0.430708 | − | 0.902491i | \(-0.358264\pi\) | ||||
0.430708 | + | 0.902491i | \(0.358264\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 6.05593i | − 0.525115i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 2.30255i | − 0.196720i | −0.995151 | − | 0.0983602i | \(-0.968640\pi\) | ||||
0.995151 | − | 0.0983602i | \(-0.0313597\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.16605 | −0.438179 | −0.219090 | − | 0.975705i | \(-0.570309\pi\) | ||||
−0.219090 | + | 0.975705i | \(0.570309\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.8330 | 0.996517 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.30684i | 0.527405i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.10798i | 0.173863i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.85936 | −0.316171 | −0.158086 | − | 0.987425i | \(-0.550532\pi\) | ||||
−0.158086 | + | 0.987425i | \(0.550532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.71103 | −0.383379 | −0.191689 | − | 0.981456i | \(-0.561397\pi\) | ||||
−0.191689 | + | 0.981456i | \(0.561397\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 44.1958i | 3.57302i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 8.30684i | 0.662958i | 0.943463 | + | 0.331479i | \(0.107548\pi\) | ||||
−0.943463 | + | 0.331479i | \(0.892452\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.69316 | 0.451497 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.1975 | −1.04011 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6348i | 1.06796i | 0.845497 | + | 0.533981i | \(0.179304\pi\) | ||||
−0.845497 | + | 0.533981i | \(0.820696\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 9.97163i | 0.771628i | 0.922577 | + | 0.385814i | \(0.126079\pi\) | ||||
−0.922577 | + | 0.385814i | \(0.873921\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.33211 | 0.256316 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 12.1690 | 0.930587 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 9.11361i | − 0.692895i | −0.938069 | − | 0.346448i | \(-0.887388\pi\) | ||||
0.938069 | − | 0.346448i | \(-0.112612\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 13.9161i | 1.04600i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 12.9403 | 0.967205 | 0.483602 | − | 0.875288i | \(-0.339328\pi\) | ||||
0.483602 | + | 0.875288i | \(0.339328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 8.16191 | 0.606670 | 0.303335 | − | 0.952884i | \(-0.401900\pi\) | ||||
0.303335 | + | 0.952884i | \(0.401900\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 8.46876i | − 0.626029i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 16.0567i | − 1.17418i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −21.0254 | −1.52937 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4.52829 | 0.327656 | 0.163828 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163828 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 14.1662i | 1.01971i | 0.860262 | + | 0.509853i | \(0.170300\pi\) | ||||
−0.860262 | + | 0.509853i | \(0.829700\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 12.5042i | − 0.890888i | −0.895310 | − | 0.445444i | \(-0.853046\pi\) | ||||
0.895310 | − | 0.445444i | \(-0.146954\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.5853 | 1.03393 | 0.516963 | − | 0.856008i | \(-0.327062\pi\) | ||||
0.516963 | + | 0.856008i | \(0.327062\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 17.4950 | 1.23400 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − 10.7229i | − 0.752597i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 26.5196i | − 1.84324i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.42111 | −0.305815 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −26.3860 | −1.81649 | −0.908245 | − | 0.418439i | \(-0.862577\pi\) | ||||
−0.908245 | + | 0.418439i | \(0.862577\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 42.1950i | − 2.89115i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 29.6348i | − 2.01174i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 27.0971 | 1.83105 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 24.6137 | 1.65570 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.89482i | 0.126886i | 0.997985 | + | 0.0634432i | \(0.0202082\pi\) | ||||
−0.997985 | + | 0.0634432i | \(0.979792\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 24.9805i | − 1.65801i | −0.559238 | − | 0.829007i | \(-0.688906\pi\) | ||||
0.559238 | − | 0.829007i | \(-0.311094\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.52549 | 0.166889 | 0.0834446 | − | 0.996512i | \(-0.473408\pi\) | ||||
0.0834446 | + | 0.996512i | \(0.473408\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 16.5106 | 1.08632 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 9.24835i | − 0.605880i | −0.953010 | − | 0.302940i | \(-0.902032\pi\) | ||||
0.953010 | − | 0.302940i | \(-0.0979681\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 0.938323i | − 0.0609507i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.34746 | −0.151844 | −0.0759222 | − | 0.997114i | \(-0.524190\pi\) | ||||
−0.0759222 | + | 0.997114i | \(0.524190\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.89068 | 0.186205 | 0.0931024 | − | 0.995657i | \(-0.470322\pi\) | ||||
0.0931024 | + | 0.995657i | \(0.470322\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.82021i | 0.437516i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 6.77721i | − 0.431224i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 10.8323 | 0.686471 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 24.9730 | 1.57628 | 0.788140 | − | 0.615496i | \(-0.211044\pi\) | ||||
0.788140 | + | 0.615496i | \(0.211044\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 9.63481i | 0.605736i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.7500i | 0.670569i | 0.942117 | + | 0.335284i | \(0.108832\pi\) | ||||
−0.942117 | + | 0.335284i | \(0.891168\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −18.2903 | −1.13650 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 21.5469 | 1.33372 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 4.90250i | 0.302301i | 0.988511 | + | 0.151151i | \(0.0482979\pi\) | ||||
−0.988511 | + | 0.151151i | \(0.951702\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 26.2754i | 1.60803i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.32797 | −0.202910 | −0.101455 | − | 0.994840i | \(-0.532350\pi\) | ||||
−0.101455 | + | 0.994840i | \(0.532350\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.58222 | 0.278350 | 0.139175 | − | 0.990268i | \(-0.455555\pi\) | ||||
0.139175 | + | 0.990268i | \(0.455555\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.3094i | 1.53179i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 24.2178i | − 1.45511i | −0.686050 | − | 0.727555i | \(-0.740657\pi\) | ||||
0.686050 | − | 0.727555i | \(-0.259343\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 59.5493 | 3.56512 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6.61369 | 0.394540 | 0.197270 | − | 0.980349i | \(-0.436792\pi\) | ||||
0.197270 | + | 0.980349i | \(0.436792\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 5.16605i | − 0.307090i | −0.988142 | − | 0.153545i | \(-0.950931\pi\) | ||||
0.988142 | − | 0.153545i | \(-0.0490690\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 2.77840i | − 0.164004i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.6645 | −2.68615 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 52.2426 | 3.06252 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.2458i | 0.598567i | 0.954164 | + | 0.299284i | \(0.0967477\pi\) | ||||
−0.954164 | + | 0.299284i | \(0.903252\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 15.3495i | 0.890671i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −14.7694 | −0.854137 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.3551 | 0.769778 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 38.1603i | 2.19225i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 18.2754i | − 1.04303i | −0.853242 | − | 0.521515i | \(-0.825367\pi\) | ||||
0.853242 | − | 0.521515i | \(-0.174633\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 23.6036 | 1.34276 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.50303 | 0.255343 | 0.127672 | − | 0.991816i | \(-0.459250\pi\) | ||||
0.127672 | + | 0.991816i | \(0.459250\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.56095i | − 0.370847i | −0.982659 | − | 0.185423i | \(-0.940634\pi\) | ||||
0.982659 | − | 0.185423i | \(-0.0593656\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.8363i | 0.720960i | 0.932767 | + | 0.360480i | \(0.117387\pi\) | ||||
−0.932767 | + | 0.360480i | \(0.882613\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.82820 | −0.438295 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −12.9375 | −0.722102 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.2543i | 0.960052i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.2738i | 3.00135i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −11.2220 | −0.618688 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8.99705 | −0.494523 | −0.247261 | − | 0.968949i | \(-0.579531\pi\) | ||||
−0.247261 | + | 0.968949i | \(0.579531\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 36.7532i | − 2.01406i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 35.0502i | − 1.90930i | −0.297723 | − | 0.954652i | \(-0.596227\pi\) | ||||
0.297723 | − | 0.954652i | \(-0.403773\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 23.6809 | 1.28617 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −21.6348 | −1.17159 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 17.4497i | 0.942195i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 18.8982i | 1.01451i | 0.861796 | + | 0.507255i | \(0.169340\pi\) | ||||
−0.861796 | + | 0.507255i | \(0.830660\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.1653 | 1.24001 | 0.620004 | − | 0.784599i | \(-0.287131\pi\) | ||||
0.620004 | + | 0.784599i | \(0.287131\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −23.5296 | −1.25592 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.55171i | 0.0825893i | 0.999147 | + | 0.0412946i | \(0.0131482\pi\) | ||||
−0.999147 | + | 0.0412946i | \(0.986852\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 64.4357i | − 3.41030i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.28128 | 0.225957 | 0.112979 | − | 0.993597i | \(-0.463961\pi\) | ||||
0.112979 | + | 0.993597i | \(0.463961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.2492 | −0.749956 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 20.1730i | 1.05881i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 15.3067i | − 0.799003i | −0.916733 | − | 0.399501i | \(-0.869183\pi\) | ||||
0.916733 | − | 0.399501i | \(-0.130817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 5.58303 | 0.290641 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.39918 | −0.280312 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.39489i | 0.279337i | 0.990198 | + | 0.139668i | \(0.0446037\pi\) | ||||
−0.990198 | + | 0.139668i | \(0.955396\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 12.0000i | − 0.618031i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −26.8009 | −1.37667 | −0.688334 | − | 0.725394i | \(-0.741658\pi\) | ||||
−0.688334 | + | 0.725394i | \(0.741658\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 13.0297 | 0.667532 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 21.6675i | − 1.10716i | −0.832797 | − | 0.553578i | \(-0.813262\pi\) | ||||
0.832797 | − | 0.553578i | \(-0.186738\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.8363i | 1.36417i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −25.7187 | −1.30399 | −0.651995 | − | 0.758223i | \(-0.726068\pi\) | ||||
−0.651995 | + | 0.758223i | \(0.726068\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 37.6017 | 1.90160 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − 28.8848i | − 1.45704i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.1603i | 1.41333i | 0.707551 | + | 0.706663i | \(0.249800\pi\) | ||||
−0.707551 | + | 0.706663i | \(0.750200\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −17.7419 | −0.888208 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −10.7178 | −0.535220 | −0.267610 | − | 0.963527i | \(-0.586234\pi\) | ||||
−0.267610 | + | 0.963527i | \(0.586234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 33.1644i | − 1.65204i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 13.3528i | 0.661873i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.7492 | −1.12488 | −0.562439 | − | 0.826839i | \(-0.690137\pi\) | ||||
−0.562439 | + | 0.826839i | \(0.690137\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.74575 | −0.332743 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 13.1975i | − 0.649408i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.1349i | 0.741159i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.02542 | 0.343214 | 0.171607 | − | 0.985165i | \(-0.445104\pi\) | ||||
0.171607 | + | 0.985165i | \(0.445104\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.5992 | 0.808996 | 0.404498 | − | 0.914539i | \(-0.367446\pi\) | ||||
0.404498 | + | 0.914539i | \(0.367446\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 22.5499i | − 1.09641i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8.03147i | 0.388670i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 18.4770 | 0.892080 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.7229 | −0.516502 | −0.258251 | − | 0.966078i | \(-0.583146\pi\) | ||||
−0.258251 | + | 0.966078i | \(0.583146\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − 31.1644i | − 1.49767i | −0.662758 | − | 0.748834i | \(-0.730614\pi\) | ||||
0.662758 | − | 0.748834i | \(-0.269386\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 10.3534i | − 0.495270i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 34.7981 | 1.66082 | 0.830411 | − | 0.557152i | \(-0.188106\pi\) | ||||
0.830411 | + | 0.557152i | \(0.188106\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.01714 | 0.191292 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.8806i | 1.22963i | 0.788673 | + | 0.614813i | \(0.210769\pi\) | ||||
−0.788673 | + | 0.614813i | \(0.789231\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.3067i | 0.534788i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −27.2231 | −1.28474 | −0.642368 | − | 0.766396i | \(-0.722048\pi\) | ||||
−0.642368 | + | 0.766396i | \(0.722048\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.02837 | −0.0955120 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 13.8018i | 0.648466i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 6.19767i | − 0.289915i | −0.989438 | − | 0.144957i | \(-0.953695\pi\) | ||||
0.989438 | − | 0.144957i | \(-0.0463045\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 59.9046 | 2.79611 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.9170 | −0.508458 | −0.254229 | − | 0.967144i | \(-0.581822\pi\) | ||||
−0.254229 | + | 0.967144i | \(0.581822\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 4.07047i | − 0.189171i | −0.995517 | − | 0.0945854i | \(-0.969847\pi\) | ||||
0.995517 | − | 0.0945854i | \(-0.0301525\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 8.63657i | − 0.399653i | −0.979831 | − | 0.199826i | \(-0.935962\pi\) | ||||
0.979831 | − | 0.199826i | \(-0.0640379\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.5916 | −0.766129 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 24.3364 | 1.12136 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 9.74989i | − 0.448300i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 10.8493i | − 0.496756i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 23.5537 | 1.07620 | 0.538098 | − | 0.842882i | \(-0.319143\pi\) | ||||
0.538098 | + | 0.842882i | \(0.319143\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −20.4688 | −0.933295 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 38.6645i | 1.75930i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.9102i | 0.902217i | 0.892469 | + | 0.451108i | \(0.148971\pi\) | ||||
−0.892469 | + | 0.451108i | \(0.851029\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 39.9456 | 1.80640 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 29.7585 | 1.34298 | 0.671490 | − | 0.741013i | \(-0.265654\pi\) | ||||
0.671490 | + | 0.741013i | \(0.265654\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.5511i | 1.37595i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 40.0162i | 1.79497i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.9297 | −0.847409 | −0.423704 | − | 0.905801i | \(-0.639270\pi\) | ||||
−0.423704 | + | 0.905801i | \(0.639270\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.2137 | 1.30517 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.93382i | 0.0862248i | 0.999070 | + | 0.0431124i | \(0.0137274\pi\) | ||||
−0.999070 | + | 0.0431124i | \(0.986273\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 9.76202i | − 0.433546i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −34.6602 | −1.53629 | −0.768144 | − | 0.640277i | \(-0.778819\pi\) | ||||
−0.768144 | + | 0.640277i | \(0.778819\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −25.6979 | −1.13681 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 16.4943i | − 0.728242i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 8.19258i | 0.360309i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26.7000 | −1.17200 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.33402 | −0.277498 | −0.138749 | − | 0.990328i | \(-0.544308\pi\) | ||||
−0.138749 | + | 0.990328i | \(0.544308\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 29.9460i | 1.30944i | 0.755869 | + | 0.654722i | \(0.227215\pi\) | ||||
−0.755869 | + | 0.654722i | \(0.772785\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 84.4341i | 3.67801i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.437142 | 0.0190062 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 26.5196 | 1.15085 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 3.10932i | − 0.134680i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 37.9110i | − 1.63598i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.45946 | −0.0628635 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.834750 | 0.0358887 | 0.0179443 | − | 0.999839i | \(-0.494288\pi\) | ||||
0.0179443 | + | 0.999839i | \(0.494288\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 23.9118i | − 1.02615i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 20.6527i | − 0.883045i | −0.897250 | − | 0.441523i | \(-0.854438\pi\) | ||||
0.897250 | − | 0.441523i | \(-0.145562\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −16.1387 | −0.688784 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.41203 | 0.358364 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.889872i | 0.0378412i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 8.72447i | − 0.369668i | −0.982770 | − | 0.184834i | \(-0.940825\pi\) | ||||
0.982770 | − | 0.184834i | \(-0.0591747\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.9458 | 0.632140 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −47.0411 | −1.98608 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 9.80144i | − 0.413081i | −0.978438 | − | 0.206541i | \(-0.933779\pi\) | ||||
0.978438 | − | 0.206541i | \(-0.0662206\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 15.0620i | 0.632546i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −25.1570 | −1.05464 | −0.527318 | − | 0.849668i | \(-0.676802\pi\) | ||||
−0.527318 | + | 0.849668i | \(0.676802\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 27.1928 | 1.13798 | 0.568992 | − | 0.822343i | \(-0.307334\pi\) | ||||
0.568992 | + | 0.822343i | \(0.307334\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 13.2664i | − 0.554214i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.365186i | − 0.0152029i | −0.999971 | − | 0.00760144i | \(-0.997580\pi\) | ||||
0.999971 | − | 0.00760144i | \(-0.00241964\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 41.5025 | 1.72478 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.2730 | −0.426196 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.94166i | 0.163247i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 37.7242i | − 1.55704i | −0.627617 | − | 0.778522i | \(-0.715970\pi\) | ||||
0.627617 | − | 0.778522i | \(-0.284030\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.2484 | 0.957932 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −36.6334 | −1.50689 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 45.1333i | 1.85340i | 0.375800 | + | 0.926701i | \(0.377368\pi\) | ||||
−0.375800 | + | 0.926701i | \(0.622632\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 42.7303i | − 1.74884i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15.4982 | −0.633238 | −0.316619 | − | 0.948553i | \(-0.602548\pi\) | ||||
−0.316619 | + | 0.948553i | \(0.602548\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −5.18924 | −0.211674 | −0.105837 | − | 0.994384i | \(-0.533752\pi\) | ||||
−0.105837 | + | 0.994384i | \(0.533752\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 33.3398i | − 1.35770i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 16.8280i | − 0.683029i | −0.939876 | − | 0.341515i | \(-0.889060\pi\) | ||||
0.939876 | − | 0.341515i | \(-0.110940\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −31.4146 | −1.27298 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −12.5586 | −0.508065 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 25.1042i | − 1.01395i | −0.861961 | − | 0.506975i | \(-0.830764\pi\) | ||||
0.861961 | − | 0.506975i | \(-0.169236\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14.3324i | 0.577001i | 0.957480 | + | 0.288501i | \(0.0931567\pi\) | ||||
−0.957480 | + | 0.288501i | \(0.906843\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −19.2712 | −0.774576 | −0.387288 | − | 0.921959i | \(-0.626588\pi\) | ||||
−0.387288 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −35.9456 | −1.44245 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 24.9186i | − 0.998344i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.9524i | 0.517271i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 52.1119 | 2.07784 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.1856 | −1.20167 | −0.600834 | − | 0.799374i | \(-0.705165\pi\) | ||||
−0.600834 | + | 0.799374i | \(0.705165\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 77.3027i | 3.07251i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 2.23724i | − 0.0886427i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −80.4100 | −3.18097 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25.9984 | −1.02687 | −0.513437 | − | 0.858127i | \(-0.671628\pi\) | ||||
−0.513437 | + | 0.858127i | \(0.671628\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 11.4402i | − 0.451159i | −0.974225 | − | 0.225580i | \(-0.927572\pi\) | ||||
0.974225 | − | 0.225580i | \(-0.0724276\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 37.6915i | 1.48181i | 0.671611 | + | 0.740904i | \(0.265603\pi\) | ||||
−0.671611 | + | 0.740904i | \(0.734397\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.63481 | −0.378200 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −86.8205 | −3.40277 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 43.6814i | 1.70938i | 0.519136 | + | 0.854692i | \(0.326254\pi\) | ||||
−0.519136 | + | 0.854692i | \(0.673746\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 51.6383i | − 2.01460i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.0900 | −0.977367 | −0.488684 | − | 0.872461i | \(-0.662523\pi\) | ||||
−0.488684 | + | 0.872461i | \(0.662523\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.7392 | −1.46788 | −0.733942 | − | 0.679212i | \(-0.762322\pi\) | ||||
−0.733942 | + | 0.679212i | \(0.762322\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 72.1102i | − 2.80053i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 18.3321i | − 0.709822i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.55121 | 0.214622 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.86335 | 0.226352 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 3.63642i | − 0.140174i | −0.997541 | − | 0.0700869i | \(-0.977672\pi\) | ||||
0.997541 | − | 0.0700869i | \(-0.0223277\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.1948i | 1.12205i | 0.827800 | + | 0.561024i | \(0.189592\pi\) | ||||
−0.827800 | + | 0.561024i | \(0.810408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −49.5450 | −1.90136 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −73.1849 | −2.80445 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 28.6527i | 1.09636i | 0.836359 | + | 0.548182i | \(0.184680\pi\) | ||||
−0.836359 | + | 0.548182i | \(0.815320\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 7.39888i | − 0.282285i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −6.04225 | −0.230191 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 17.6880 | 0.672883 | 0.336442 | − | 0.941704i | \(-0.390777\pi\) | ||||
0.336442 | + | 0.941704i | \(0.390777\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 31.4638i | − 1.19521i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.91609i | 0.299843i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −27.0947 | −1.02482 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.79339 | 0.105505 | 0.0527525 | − | 0.998608i | \(-0.483201\pi\) | ||||
0.0527525 | + | 0.998608i | \(0.483201\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 14.3486i | − 0.541169i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − 36.1899i | − 1.36106i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −20.4117 | −0.766578 | −0.383289 | − | 0.923628i | \(-0.625209\pi\) | ||||
−0.383289 | + | 0.923628i | \(0.625209\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.78814 | −0.0670606 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 50.6645i | − 1.89740i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 6.87730i | 0.256838i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −34.9848 | −1.30471 | −0.652356 | − | 0.757912i | \(-0.726219\pi\) | ||||
−0.652356 | + | 0.757912i | \(0.726219\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.3849 | −0.833655 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 8.46876i | − 0.314957i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 24.8796i | − 0.922734i | −0.887209 | − | 0.461367i | \(-0.847359\pi\) | ||||
0.887209 | − | 0.461367i | \(-0.152641\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.2444 | 1.34238 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −38.0508 | −1.40736 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.7737i | 1.06278i | 0.847127 | + | 0.531390i | \(0.178330\pi\) | ||||
−0.847127 | + | 0.531390i | \(0.821670\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 12.1127i | 0.446176i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.1856 | 1.11039 | 0.555197 | − | 0.831719i | \(-0.312643\pi\) | ||||
0.555197 | + | 0.831719i | \(0.312643\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.8551 | −0.729394 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.7127i | 0.833247i | 0.909079 | + | 0.416624i | \(0.136787\pi\) | ||||
−0.909079 | + | 0.416624i | \(0.863213\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 20.6429i | − 0.755286i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.2695 | 0.448317 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.0200854 | −0.000732927 0 | −0.000366463 | − | 1.00000i | \(-0.500117\pi\) | ||||
−0.000366463 | 1.00000i | \(0.500117\pi\) | ||||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 73.1628i | − 2.66620i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.9002i | 1.63192i | 0.578106 | + | 0.815962i | \(0.303792\pi\) | ||||
−0.578106 | + | 0.815962i | \(0.696208\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 28.2269 | 1.02457 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.0203 | −0.689486 | −0.344743 | − | 0.938697i | \(-0.612034\pi\) | ||||
−0.344743 | + | 0.938697i | \(0.612034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 51.4713i | − 1.86339i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 14.7694i | − 0.533292i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −42.1220 | −1.51896 | −0.759480 | − | 0.650531i | \(-0.774546\pi\) | ||||
−0.759480 | + | 0.650531i | \(0.774546\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 31.4942 | 1.13424 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 10.7753i | − 0.387561i | −0.981045 | − | 0.193780i | \(-0.937925\pi\) | ||||
0.981045 | − | 0.193780i | \(-0.0620749\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 53.5848i | 1.92234i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.17964 | 0.0780938 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 29.2137 | 1.04535 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 29.2055i | − 1.04372i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 22.8592i | 0.814843i | 0.913240 | + | 0.407421i | \(0.133572\pi\) | ||||
−0.913240 | + | 0.407421i | \(0.866428\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 14.3628 | 0.511328 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.4581 | −0.798519 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.98805i | 0.319175i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 5.00444i | − 0.177266i | −0.996064 | − | 0.0886332i | \(-0.971750\pi\) | ||||
0.996064 | − | 0.0886332i | \(-0.0282499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 31.9731 | 1.13113 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 50.0724 | 1.76922 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 18.7607i | 0.662050i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.74989i | 0.343212i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −7.52135 | −0.264437 | −0.132218 | − | 0.991221i | \(-0.542210\pi\) | ||||
−0.132218 | + | 0.991221i | \(0.542210\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 29.4103 | 1.03273 | 0.516367 | − | 0.856367i | \(-0.327284\pi\) | ||||
0.516367 | + | 0.856367i | \(0.327284\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 13.4244i | − 0.470816i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 10.4770i | 0.366545i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 48.2315 | 1.68535 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.0205 | 1.32692 | 0.663462 | − | 0.748210i | \(-0.269087\pi\) | ||||
0.663462 | + | 0.748210i | \(0.269087\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − 25.7849i | − 0.898805i | −0.893329 | − | 0.449403i | \(-0.851637\pi\) | ||||
0.893329 | − | 0.449403i | \(-0.148363\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 7.00295i | 0.243516i | 0.992560 | + | 0.121758i | \(0.0388533\pi\) | ||||
−0.992560 | + | 0.121758i | \(0.961147\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.166709 | −0.00579003 | −0.00289501 | − | 0.999996i | \(-0.500922\pi\) | ||||
−0.00289501 | + | 0.999996i | \(0.500922\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −70.9505 | −2.46125 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 5.69584i | 0.197349i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 80.7154i | − 2.78993i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.1105 | 0.452625 | 0.226313 | − | 0.974055i | \(-0.427333\pi\) | ||||
0.226313 | + | 0.974055i | \(0.427333\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.1053 | −0.486391 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 19.3760i | − 0.667345i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 19.1313i | − 0.657361i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −15.1349 | −0.519428 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −31.2696 | −1.07191 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.445573i | 0.0152561i | 0.999971 | + | 0.00762806i | \(0.00242811\pi\) | ||||
−0.999971 | + | 0.00762806i | \(0.997572\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 20.5519i | − 0.702038i | −0.936368 | − | 0.351019i | \(-0.885835\pi\) | ||||
0.936368 | − | 0.351019i | \(-0.114165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 18.8891 | 0.644487 | 0.322243 | − | 0.946657i | \(-0.395563\pi\) | ||||
0.322243 | + | 0.946657i | \(0.395563\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −8.13983 | −0.277405 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 47.9204i | 1.63123i | 0.578596 | + | 0.815614i | \(0.303601\pi\) | ||||
−0.578596 | + | 0.815614i | \(0.696399\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 133.782i | 4.54349i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.649649 | 0.0220378 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.5677 | −0.629144 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 99.5576i | − 3.36951i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 50.2738i | − 1.69762i | −0.528694 | − | 0.848812i | \(-0.677318\pi\) | ||||
0.528694 | − | 0.848812i | \(-0.322682\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.0170 | 1.01245 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.6019 | −1.30053 | −0.650265 | − | 0.759707i | \(-0.725342\pi\) | ||||
−0.650265 | + | 0.759707i | \(0.725342\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 3.07860i | − 0.103603i | −0.998657 | − | 0.0518016i | \(-0.983504\pi\) | ||||
0.998657 | − | 0.0518016i | \(-0.0164963\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 31.0770i | − 1.04346i | −0.853110 | − | 0.521731i | \(-0.825286\pi\) | ||||
0.853110 | − | 0.521731i | \(-0.174714\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.3569 | −0.414437 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 10.9960 | 0.368380 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 8.80358i | − 0.294601i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 43.2696i | 1.44473i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 41.1644 | 1.37291 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.3831 | 0.512485 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 39.1263i | − 1.30204i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 42.5534i | 1.41296i | 0.707731 | + | 0.706482i | \(0.249719\pi\) | ||||
−0.707731 | + | 0.706482i | \(0.750281\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 72.7213 | 2.41201 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −14.8694 | −0.492645 | −0.246323 | − | 0.969188i | \(-0.579222\pi\) | ||||
−0.246323 | + | 0.969188i | \(0.579222\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 7.49977i | 0.248206i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 27.3933i | 0.904606i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −26.5539 | −0.875931 | −0.437965 | − | 0.898992i | \(-0.644301\pi\) | ||||
−0.437965 | + | 0.898992i | \(0.644301\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.5410 | −1.76424 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 44.7823i | 1.47403i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 44.9810i | − 1.47737i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.70749 | −0.0888298 | −0.0444149 | − | 0.999013i | \(-0.514142\pi\) | ||||
−0.0444149 | + | 0.999013i | \(0.514142\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.56831 | 0.0513993 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 13.1924i | − 0.431901i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 36.0067i | − 1.17629i | −0.808757 | − | 0.588143i | \(-0.799859\pi\) | ||||
0.808757 | − | 0.588143i | \(-0.200141\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.2215 | −0.627269 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11.6135 | 0.378591 | 0.189295 | − | 0.981920i | \(-0.439380\pi\) | ||||
0.189295 | + | 0.981920i | \(0.439380\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 4.75004i | − 0.154683i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 20.9061i | − 0.679355i | −0.940542 | − | 0.339678i | \(-0.889682\pi\) | ||||
0.940542 | − | 0.339678i | \(-0.110318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.7586 | −0.933544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 37.6063 | 1.21947 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 13.7510i | 0.445438i | 0.974883 | + | 0.222719i | \(0.0714933\pi\) | ||||
−0.974883 | + | 0.222719i | \(0.928507\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 22.9341i | 0.741355i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6.39742 | 0.206584 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 82.7663 | 2.66988 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.6547i | 0.794488i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.07935i | 0.227656i | 0.993500 | + | 0.113828i | \(0.0363114\pi\) | ||||
−0.993500 | + | 0.113828i | \(0.963689\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 50.5494 | 1.62388 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.7382 | −0.601338 | −0.300669 | − | 0.953729i | \(-0.597210\pi\) | ||||
−0.300669 | + | 0.953729i | \(0.597210\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − 14.3534i | − 0.460148i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 60.6756i | 1.94118i | 0.240729 | + | 0.970592i | \(0.422613\pi\) | ||||
−0.240729 | + | 0.970592i | \(0.577387\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −18.1918 | −0.581412 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 103.428 | 3.30221 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 47.3720i | − 1.51093i | −0.655188 | − | 0.755466i | \(-0.727410\pi\) | ||||
0.655188 | − | 0.755466i | \(-0.272590\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 32.8768i | 1.04648i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 22.8323 | 0.726026 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.2110 | −0.610256 | −0.305128 | − | 0.952311i | \(-0.598699\pi\) | ||||
−0.305128 | + | 0.952311i | \(0.598699\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 26.3585i | 0.836461i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 59.1077i | − 1.87196i | −0.352053 | − | 0.935980i | \(-0.614516\pi\) | ||||
0.352053 | − | 0.935980i | \(-0.385484\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −49.8167 | −1.57613 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 4100.2.d.c.1149.2 | 8 | ||
5.2 | odd | 4 | 4100.2.a.c.1.1 | 4 | |||
5.3 | odd | 4 | 164.2.a.a.1.4 | ✓ | 4 | ||
5.4 | even | 2 | inner | 4100.2.d.c.1149.7 | 8 | ||
15.8 | even | 4 | 1476.2.a.g.1.4 | 4 | |||
20.3 | even | 4 | 656.2.a.i.1.1 | 4 | |||
35.13 | even | 4 | 8036.2.a.i.1.1 | 4 | |||
40.3 | even | 4 | 2624.2.a.y.1.4 | 4 | |||
40.13 | odd | 4 | 2624.2.a.v.1.1 | 4 | |||
60.23 | odd | 4 | 5904.2.a.bp.1.4 | 4 | |||
205.163 | odd | 4 | 6724.2.a.c.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
164.2.a.a.1.4 | ✓ | 4 | 5.3 | odd | 4 | ||
656.2.a.i.1.1 | 4 | 20.3 | even | 4 | |||
1476.2.a.g.1.4 | 4 | 15.8 | even | 4 | |||
2624.2.a.v.1.1 | 4 | 40.13 | odd | 4 | |||
2624.2.a.y.1.4 | 4 | 40.3 | even | 4 | |||
4100.2.a.c.1.1 | 4 | 5.2 | odd | 4 | |||
4100.2.d.c.1149.2 | 8 | 1.1 | even | 1 | trivial | ||
4100.2.d.c.1149.7 | 8 | 5.4 | even | 2 | inner | ||
5904.2.a.bp.1.4 | 4 | 60.23 | odd | 4 | |||
6724.2.a.c.1.1 | 4 | 205.163 | odd | 4 | |||
8036.2.a.i.1.1 | 4 | 35.13 | even | 4 |